Up 8-7 at halftime, the Hurricanes scored three tries after the break to notch a sixth win from seven games, to move ahead of the unbeaten Chiefs on points differential.
The Chiefs sat out a bye in round seven and return to the fray next week against the Hurricanes, in what will be a table-topping affair in Wellington on Saturday.
Winger Salesi Rayasi bagged a try in each half while the other tries were scored by two in-form players in lock James Blackwell and halfback Cam Roigard as the speed of the Hurricanes' phase play proved too much for the hosts during a purple patch early in the second spell.
Roigard and centre Billy Proctor were the best attackers on show in a high-octane affair although the Hurricanes will be disappointed not to secure a bonus point after conceding a late try to Highlanders flanker Billy Harmon.
The result ends a three-match winning run for the Highlanders, who remain sixth in the standings.